Average Consensus Filter Research Articles

Consensus-Based Distributed Batch Estimation in Asynchronous Wireless Sensor Networks

In this paper, to address the distributed estimation problem over an asynchronous wireless sensor network (aWSN), an average consensus-based distributed batch estimation (DBE) method is proposed. The DBE seeks to update the global posterior with a predefined global update period (GUP) and is implemented with a local filter (LF) and a fusion filter (FF). For LF, we develop two different asynchronous batch estimation approaches to align and compute the asynchronous local posteriors of multiple nodes in an aWSN. At FF, an average consensus filter is adopted to compute the global posterior via a proposed DBE fusion rule. Numerical results show that the proposed DBE method has high target-tracking accuracy and is robust to strong asynchronism. Besides, the optimality of DBE fusion can be approximately achieved with a sufficiently large number of particles and consensus iterations.

A Tracking Algorithm for Sparse and Dynamic Underwater Sensor Networks

An underwater sensor network (UWSN) has sparse and dynamic characteristics. In sparse and dynamic UWSNs, the traditional particle filter based on multi-rate consensus/fusion (CF/DPF) has the problems of a slow convergence rate and low filtering accuracy. To solve these problems, a tracking algorithm for sparse and dynamic UWSNs based on particle filter (TASD) is proposed. Firstly, the estimation results of a local particle filter are processed by a weighted average consensus filter (WACF). In this way, the reliability difference of state estimation between nodes in sparse and dynamic UWSN is reasonably eliminated. Secondly, a delayed update mechanism (DUM) is added to WACF, which effectively solves the problem of time synchronization between the two particle filters. Thirdly, under the condition of limited communication energy consumption, an alternating random scheme (ARS) is designed, which optimizes the mean square convergence rate of the fusion particle filter. Simulation results show that the proposed algorithm can be applied to maneuvering target tracking in sparse and dynamic UWSN effectively. Compared with the traditional method, it has higher tracking accuracy and faster convergence speed. The average estimation error of TASD is 91.3% lower than that of CF/DPF, and the weighted consensus tracking error of TASD is reduced by 85.6% compared with CF/DPF.

A Distributed Probabilistic Modeling Algorithm for the Aggregated Power Forecast Error of Multiple Newly Built Wind Farms

The extensive penetration of wind farms (WFs) presents challenges to the operation of distribution networks (DNs). Building a probability distribution of the aggregated wind power forecast error is of great value for decision making. However, as a result of recent government incentives, many WFs are being newly built with little historical data for training distribution models. Moreover, WFs with different stakeholders may refuse to submit the raw data to a data center for model training. To address these problems, a Gaussian mixture model (GMM) is applied to build the distribution of the aggregated wind power forecast error; then, the maximum a posteriori (MAP) estimation method is adopted to overcome the limited training data problem in GMM parameter estimation. Next, a distributed MAP estimation method is developed based on the average consensus filter algorithm to address the data privacy issue. The distribution control center is introduced into the distributed estimation process to acquire more precise estimation results and better adapt to the DN control architecture. The effectiveness of the proposed algorithm is empirically verified using historical data.

Distributed Kalman filtering for Time-Space Gaussian Processes

In this paper we address the problem of distributed Kalman filtering for spatio-temporal Gaussian Process (GP) regression. We start our analysis from a recent result that bridges classical non-parametric GP-based regression and recursive Kalman filtering. Inspired by results on distributed Kalman filtering, we propose two algorithms to perform distributed GP regression in sensor networks. In the first procedure each sensor estimates a local copy of the entire process by combining a classical average consensus information filter running among neighboring sensors with local Kalman filter which is optimal with respect to the partial information gathered by means of the consensus. The procedure, in the limit of the average consensus filter, is proven to be in one-to-one correspondence with the classical centralized Kalman procedure. To enhance the estimation performance, in the second algorithm neighboring nodes perform consensus among the partial state estimates. Finally, theoretical results are complemented with numerical simulations and compared with solutions available in the literature.

Distributed Particle Filter for Target Tracking: With Reduced Sensor Communications

For efficient and accurate estimation of the location of objects, a network of sensors can be used to detect and track targets in a distributed manner. In nonlinear and/or non-Gaussian dynamic models, distributed particle filtering methods are commonly applied to develop target tracking algorithms. An important consideration in developing a distributed particle filtering algorithm in wireless sensor networks is reducing the size of data exchanged among the sensors because of power and bandwidth constraints. In this paper, we propose a distributed particle filtering algorithm with the objective of reducing the overhead data that is communicated among the sensors. In our algorithm, the sensors exchange information to collaboratively compute the global likelihood function that encompasses the contribution of the measurements towards building the global posterior density of the unknown location parameters. Each sensor, using its own measurement, computes its local likelihood function and approximates it using a Gaussian function. The sensors then propagate only the mean and the covariance of their approximated likelihood functions to other sensors, reducing the communication overhead. The global likelihood function is computed collaboratively from the parameters of the local likelihood functions using an average consensus filter or a forward-backward propagation information exchange strategy.

Distributed Maximum Likelihood Classification of Linear Modulations Over Nonidentical Flat Block-Fading Gaussian Channels

In this paper, we consider distributed maximum likelihood (ML) classification of digital amplitude-phase modulated signals using multiple sensors that observe the same sequence of unknown symbol transmissions over nonidentical flat blockfading Gaussian noise channels. A variant of the expectation-maximization (EM) algorithm is employed to obtain the ML estimates of the unknown channel parameters and compute the global log-likelihood of the observations received by all the sensors in a distributed manner by means of an average consensus filter. This procedure is repeated for all candidate modulation formats in the reference library, and a classification decision, which is available at any of the sensors in the network, is declared in favor of the modulation with the highest log-likelihood score. The proposed scheme improves the classification accuracy by exploiting the signal-to-noise ratio (SNR) diversity in the network while restricting the communication to a small neighborhood of each sensor. Numerical examples show that the proposed distributed EM-based classifier can achieve the same classification performance as that of a centralized classifier, which has all the sensor measurements, for a wide range of SNR values.

Distributed Sensor Fusion for Scalar Field Mapping Using Mobile Sensor Networks

In this paper, autonomous mobile sensor networks are deployed to measure a scalar field and build its map. We develop a novel method for multiple mobile sensor nodes to build this map using noisy sensor measurements. Our method consists of two parts. First, we develop a distributed sensor fusion algorithm by integrating two different distributed consensus filters to achieve cooperative sensing among sensor nodes. This fusion algorithm has two phases. In the first phase, the weighted average consensus filter is developed, which allows each sensor node to find an estimate of the value of the scalar field at each time step. In the second phase, the average consensus filter is used to allow each sensor node to find a confidence of the estimate at each time step. The final estimate of the value of the scalar field is iteratively updated during the movement of the mobile sensors via weighted average. Second, we develop the distributed flocking-control algorithm to drive the mobile sensors to form a network and track the virtual leader moving along the field when only a small subset of the mobile sensors know the information of the leader. Experimental results are provided to demonstrate our proposed algorithms.

Distributed consensus filtering for discrete-time nonlinear systems with non-Gaussian noise

This paper studies the problem of distributed estimation for a class of discrete-time nonlinear non-Gaussian systems in a not fully connected sensor network environment. The non-Gaussian process noise and measurement noise are approximated by finite Gaussian mixture models. A distributed Gaussian mixture unscented Kalman filter (UKF) is developed in which each sensor node independently calculates local statistics by using its own measurement and an average-consensus filter is utilized to diffuse local statistics to its neighbors. A main difficulty encountered is the distributed computation of the Gaussian mixture weights, which is overcome by introducing the natural logarithm transformation. The effectiveness of the proposed distributed filter is verified via a simulation example involving tracking a target in the presence of glint noise.

Distributed Particle Filter for Nonlinear Hybrid Systems Based on Average Consensus Filter

AbstractThis paper presents a new distributed monitoring approach for nonlinear, non-Gaussian hybrid systems incorporating multiple sensors in an embedded network configuration. The estimation engine of the proposed approach is particle filter (PF) which estimates locally the mode and continuous state of hybrid system at each sensor location or node. Decision on the mode of the system is established locally in a distributed network in which only nearby nodes exchange information. This objective is obtained by using an average consensus filter that allows the nodes of the system to reach agreement on values acquired by the nodes of the network. The effectiveness of the proposed method is demonstrated through simulation studies.

Distributed multi-target tracking using joint probabilistic data association and average consensus filter

In this paper, a distributed multi-target tracking (MTT) algorithm suitable for implementation in wireless sensor networks is proposed. For this purpose, the Monte Carlo (MC) implementation of joint probabilistic data-association filter (JPDAF) is applied to the well-known problem of multi-target tracking in a cluttered area. Also, to make the tracking algorithm scalable and usable for sensor networks of many nodes, the distributed expectation maximization algorithm is exploited via the average consensus filter, in order to diffuse the nodes’ information over the whole network. The proposed tracking system is robust and capable of modeling any state space with nonlinear and non-Gaussian models for target dynamics and measurement likelihood, since it uses the particle-filtering methods to extract samples from the desired distributions. To encounter the data-association problem that arises due to the unlabeled measurements in the presence of clutter, the well-known JPDAF algorithm is used. Furthermore, some simplifications and modifications are made to MC–JPDAF algorithm in order to reduce the computation complexity of the tracking system and make it suitable for low-energy sensor networks. Finally, the simulations of tracking tasks for a sample network are given.

Stochastic Average Consensus Filter for Distributed HMM Filtering: Almost Sure Convergence

In this paper, we study almost sure convergence of a dynamic average consensus algorithm which allows distributed computation of the product of n time-varying conditional probability density functions. These density functions (often called as “belief functions”) correspond to the conditional probability of observations given the state of an underlying Markov chain, which is observed by n different nodes within a sensor network. The topology of the sensor network is modeled as an undirected graph. The average consensus algorithm is used to obtain a distributed state estimation scheme for a hidden Markov model (HMM). We use the ordinary differential equation (ODE) technique to analyze the convergence of a stochastic approximation type algorithm for achieving average consensus with a constant step size. It is shown that, for a connected graph, under mild assumptions on the first and second moments of the observation probability densities and a geometric ergodicity condition on an extended Markov chain, the consensus filter state of each individual sensor converges almost surely to the true average of the logarithm of the belief functions of all the sensors. Convergence is proved by using a perturbed stochastic Lyapunov function technique. Numerical results suggest that the distributed estimates of the Markov chain state obtained at the individual sensor nodes based on this consensus algorithm track the centralized state estimate (computed on the basis of having access to the observations of all the nodes) quite well, while more formal results on convergence of the distributed HMM filter to the centralized one are currently under investigation.

TARGET TRACKING BY USING PARTICLE FILTER IN SENSOR NETWORKS

This paper presents a distributed particle filter (DPF) over sensor networks. We propose two major steps to make a particle filter to work in a distributed way. The first step is the estimation of global mean and covariance of weighted particles by using an average consensus filter. Through this consensus filter, each sensor node can gradually diffuse its local mean and covariance of weighted particles over the entire network and asymptotically obtain the estimated global mean and covariance. The second step is the propagation of the estimated global mean and covariance through state transition distribution and likelihood distribution by using an unscented transformation (UT). Through this transformation, partial high order information of the estimated global mean and covariance can be incorporated into the estimates for non-linear models. Simulations of tracking tasks in a sensor network with 100 sensor nodes are given.